Chemical dynamics in condensed phases: relaxation, transfer and reactions in condensed molecular systems
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
2013
|
| Edition: | 1. publ. in paperback |
| Series: | Oxford graduate texts
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXII, 719 S. graph. Darst. |
| ISBN: | 9780199686681 9780198529798 |
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| 020 | |a 9780199686681 |c pbk. |9 978-0-19-968668-1 | ||
| 020 | |a 9780198529798 |c hbk |9 978-0-19-852979-8 | ||
| 035 | |a (OCoLC)885229357 | ||
| 035 | |a (DE-599)BSZ395150051 | ||
| 040 | |a DE-604 |b ger | ||
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| 084 | |a VE 9400 |0 (DE-625)147154:253 |2 rvk | ||
| 100 | 1 | |a Nitzan, Abraham |d 1944- |e Verfasser |0 (DE-588)131744593 |4 aut | |
| 245 | 1 | 0 | |a Chemical dynamics in condensed phases |b relaxation, transfer and reactions in condensed molecular systems |c Abraham Nitzan |
| 250 | |a 1. publ. in paperback | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2013 | |
| 300 | |a XXII, 719 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Oxford graduate texts | |
| 650 | 4 | |a Molecular dynamics | |
| 650 | 4 | |a Chemical reaction, Conditions and laws of | |
| 650 | 0 | 7 | |a Chemische Reaktion |0 (DE-588)4009853-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Molekulardynamik |0 (DE-588)4170370-4 |2 gnd |9 rswk-swf |
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| 689 | 0 | |8 1\p |5 DE-604 | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027218276&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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| _version_ | 1804152081485922304 |
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| adam_text | CONTENTS
PART I BACKGROUND I
1
Review of some mathematical and physical subjects
3
1.1
Mathematical background
3
1.1.1
Random variables and probability distributions
3
1.1.2
Constrained
extrema
6
1.1.3
Vector and fields
7
1.1.4
Continuity equation for the flow of conserved entities
10
1.1.5
Delta functions
11
1.1.6
Complex integration
13
1.1.7
Laplace transform
15
1.1.8
The
Schwarz
inequality
16
1.2
Classical mechanics
18
1.2.1
Classical equations of motion
18
1.2.2
Phase space, the classical distribution function, and
the Liouville equation
19
1.3
Quantum mechanics
22
1.4
Thermodynamics and statistical mechanics
25
1.4.1
Thermodynamics
25
1.4.2
Statistical mechanics
29
1.4.3
Quantum distributions
34
1.4.4
Coarse graining
35
1.5
Physical
observables as
random variables
38
1.5.1
Origin of randomness in physical systems
38
1.5.2
Joint probabilities, conditional probabilities, and
reduced descriptions
39
1.5.3
Random functions
41
1.5.4
Correlations
41
1.5.5
Diffusion
43
1.6
Electrostatics
45
1.6.1
Fundamental equations of electrostatics
45
1.6.2
Electrostatics in continuous dielectric media
47
1.6.3
Screening by mobile charges
52
xjv
Con
unis
2
Quantum
dynamics
using the time-dependent
Schrödinger
equation
57
2.1
Formal solutions
57
2.2
An example: The two-level system
59
2.3
Time-dependent Hamiltonians
63
2.4
A two-level system in a time-dependent field
66
2.5
A digression on nuclear potential surfaces
71
2.6
Expressing the time evolution in terms of the Green s operator
74
2.7
Representations
76
2.7.1
The
Schrödinger
and
Heisenberg
representations
76
2.7.2
The interaction representation
77
2.7.3
Time-dependent perturbation theory
78
2.8
Quantum dynamics of the free particles
80
2.8.1
Free particle
eigen
functions
80
2.8.2
Free particle density of slates
82
2.8.3
Time evolution of a one-dimensional free particle
wavepacket
83
2.8.4
The quantum mechanical llux
86
2.9
Quantum dynamics of the harmonic oscillator
89
2.9.1
Elementary considerations
89
2.9.2
The raising/lowering operators formalism
93
2.9.3
The
Heisenberg
equations of motion
95
2.9.4
The shifted harmonic oscillator
96
2.9.5
Harmonic oscillator at thermal equilibrium
Ю0
2.10
Tunneling
101
2.10.1
Tunneling through a square barrier
Ю1
2.10.2
Some observations
105
2A Some operator identities
109
3
An Overview of Quantum Electrodynamics and Matter-Radiation
Field Interaction
112
3.1
Introduction
П2
3.2
The quantum radiation field H4
3.2.1
Classical electrodynamics
Ц4
3.2.2
Quantum electrodynamics
1^
3.2.3
Spontaneous emission
1^
ЗА
The radiation field and its interaction with matter l2°
4
Introduction to solids and their interfaces l31
4.1
Lattice periodicity
Contents
xv
4.2
Lattice vibrations
132
4.2.1
Normal modes of harmonic systems
132
4.2.2
Simple harmonic crystal in one dimension
134
4.2.3
Density of modes
137
4.2.4
Phonons in higher dimensions and the heat capacity
ofsolids
139
4.3
Electronic structure of solids
143
4.3.1
The free electron theory of metals: Energetics
143
4.3.2
The free electron theory of metals: Motion
145
4.3.3
Electronic structure of periodic solids: Bloch theory
147
4.3.4
The one-dimensional tight binding model
150
4.3.5
The nearly free particle model
152
4.3.6
Intermediate summary: Free electrons versus
noninteracting electrons in a periodic potential
155
4.3.7
Further dynamical implications of the electronic
band structure ofsolids
157
4.3.8
Semiconductors
159
4.4
The work function
164
4.5
Surface potential and screening
167
4.5.1
General considerations
167
4.5.2
The Thomas-Fermi theory of screening by metallic
electrons
168
4.5.3
Semiconductor interfaces
170
4.5.4
Interfacial
potential distributions
173
5
Introduction to liquids
175
5.1
Statistical mechanics of classical liquids
176
5.2
Time and ensemble average
177
5.3
Reduced configurational distribution functions
179
5.4
Observable implications of the pair correlation function
182
5.4.1
X-ray scattering
182
5.4.2
The average energy
184
5.4.3
Pressure
185
5.5
The potential of mean force and the reversible work theorem
186
5.6
The virial expansion
—
the second virial coefficient
188
Partii
METHODS
191
6
Time correlation functions
193
6.1
Stationary systems
193
6.2
Simple examples
195
xvj
Conti-mi
s
6.2.1
The diffusion coefficient
195
6.2.2
Golden
rule
rates
197
6.2.3
Optical
absorption lineshapes
199
6.3
Classical time correlation functions
201
6.4
Quantum time correlation functions
206
6.5
Harmonic reservoir
209
6.5.1
Classical bath
210
6.5.2
The spectral density
213
6.5.3
Quantum bath
214
6.5.4
Why are harmonic baths models useful?
215
7
Introduction to stochastic processes
219
7.1
The nature of stochastic processes
219
7.2
Stochastic modeling of physical processes
223
7.3
The random walk problem
225
7.3.1
Time evolution
225
7.3.2
Moments
227
7.3.3
The probability distribution
230
7.4
Some concepts from the general theory of stochastic processes
233
7.4.1
Distributions and correlation functions
233
7.4.2
Markovian stochastic processes
235
7.4.3
Gaussian stochastic processes
238
7.4.4
A digression on
cumulant
expansions
241
7.5
Harmonic analysis
242
7.5.1
The power spectrum
242
7.5.2
The Wiener Khintchine theorem
244
7.5.3
Application to absorption
245
7.5.4
The power spectrum of a randomly modulated
harmonic oscillator
247
7A Moments of the Gaussian distribution
250
7B Proof of Eqs
(7.64)
and
(7.65) 251
7C
Cumulant
expansions
252
7D Proof of the Wiener Khintchine theorem
253
8
Stochastic equations of motion
255
8.1
Introduction
255
8.2
The
Langevin
equation
259
8.2.1
General considerations ^
8.2.2
The high friction limit
CONTKNTS
xvii
8.2.3
Harmonie
analysis
of the
Langevin
equation
264
8.2.4
The absorption lineshape of a harmonic oscillator
265
8.2.5
Derivation of the
Langevin
equation from
a microscopic model
267
8.2.6
The generalized
Langevin
equation
271
8.3
Master equations
273
8.3.1
The random walk problem revisited
274
8.3.2
Chemical kinetics
276
8.3.3
The relaxation of a system of harmonic
oscillators
278
8.4
The Fokker-Planck equation
281
8.4.1
A simple example
282
8.4.2
The probability flux
283
8.4.3
Derivation of the Fokker-Planck equation
from the Chapman-Kolmogorov equation
284
8.4.4
Derivation of the Smoluchowski equation
from the
Langevin
equation: The overdamped limit
287
8.4.5
Derivation of the Fokker-Planck equation
from the
Langevin
equation
290
8.4.6
The multidimensional Fokker-Planck equation
292
8.5
Passage time distributions and the mean first passage time
293
8A Obtaining the Fokker-Planck equation from the
Chapman-Kolmogorov equation
296
8B Obtaining the Smoluchowski equation from the overdamped
Langevin
equation
299
8C Derivation of the
Fokker-Planck
equation from the
Langevin
equation
301
Introduction to quantum relaxation processes
304
9.1
A simple quantum-mechanical model for relaxation
305
9.2
The origin of irreversibility
312
9.2.1
Irreversibility reflects restricted observation
312
9.2.2
Relaxation in isolated molecules
312
9.2.3
Spontaneous emission
314
9.2.4
Preparation of the initial state
315
9.3
The effect of relaxation on absorption lineshapes
316
9.4
Relaxation of a quantum harmonic oscillator
322
9.5
Quantum mechanics of steady states
329
9.5.1
Quantum description of steady-state processes
329
9.5.2
Steady-state absorption
334
9.5.3
Resonance tunneling
334
XVIII
CoNľhNTS
9A
Using projection operators
338
9B Evaluation of the absorption lineshape for the model
ofFigs9.2and9.3
34
L
9C Resonance tunneling in three dimensions
342
10
Quantum mechanical density operator
347
10.1
The density operator and the quantum
Liouville equation
348
10.1.1
The density matrix fora pure system
348
10.1.2
Statistical mixtures
349
10.1.3
Representations
351
10.1.4
Coherences
354
10.1.5
Thermodynamic equilibrium
355
10.2
An example: The time evolution of a two-level system in the
density matrix formalism
356
10.3
Reduced descriptions
359
10.3.1
General considerations
359
10.3.2
A simple example the quantum mechanical basis
for macroscopic rate equations
363
10.4
Time evolution equations for reduced density operators:
The quantum master equation
368
10.4.1
Using projection operators
368
10.4.2
The Nakajima
Zwanzig
equation
369
10.4.3
Derivation of the quantum master equation using
the thermal projector
372
10.4.4
The quantum master equation in the interaction
representation
374
10.4.5
The quantum master equation in the
Schrödinger
representation
377
10.4.6
A pause for reflection
378
10.4.7
System-states representation
379
10.4.8
The Markovian limit the Red field equation
381
10.4.9
Implications of the Redfield equation
384
10.4.10
Some general issues
388
10.5
The two-level system revisited
390
10.5.1
The two-level system in a thermal environment
390
10.5.2
The optically driven two-level system in a thermal
environment
—
the Bloch equations
392
10A Analogy of a coupled 2-level system to a spin
5
system in
a magnetic field
395
Contents
xix
11
Linear response theory
399
11.1
Classical linear response theory
400
11.1.1
Static response
400
11.1.2
Relaxation
401
11.1.3
Dynamic response
403
11.2
Quantum linear response theory
404
11.2.1
Static quantum response
405
11.2.2
Dynamic quantum response
407
11.2.3
Causality and the Kramers-Kronig relations
410
11.2.4
Examples: mobility, conductivity, and diffusion
412
11A The
Kubo
identity
417
12
The Spin-Boson Model
419
12.1
Introduction
420
12.2
The model
421
12.3
The polaron transformation
424
12.3.1
The Born
Oppenheimer
picture
426
12.4
Golden-rule transition rates
430
12.4.1
The decay of an initially prepared level
430
12.4.2
The thermally averaged rate
435
12.4.3
Evaluation of rates
436
12.5
Transition between molecular electronic states
439
12.5.1
The optical absorption lineshape
439
12.5.2
Electronic relaxation of excited molecules
442
12.5.3
The weak coupling limit and the energy gap law
443
12.5.4
The thermal activation/potential-crossing limit
445
12.5.5
Spin-lattice relaxation
446
12.6
Beyond the golden rule
449
Partili
APPLICATIONS
451
13
Vibrational energy relaxation
453
13.1
General observations
453
13.2
Construction of a model Hamiltonian
457
13.3
The vibrational relaxation rate
460
13.4
Evaluation of vibrational relaxation rates
464
13.4.1
The bilinear interaction model
464
13.4.2
Nonlinear interaction models
467
13.4.3
The independent binary collision (IBC) model
468
13.5
Multi-p
honon
theory of vibrational relaxation
471
13.6
Effect of supporting modes
476
13.7
Numerical simulations of vibrational relaxation
478
13.8
Concluding remarks
481
xx
Conîiînts
14
Chemical
reactions in condensed phases
483
14.1
Introduction
^83
14.2
Unimolecular reactions
484
14.3
Transition state theory
489
14.3Л
Foundations of TST
489
14.3.2
Transition state rate of escape from
a one-dimensional well
491
14.3.3
Transition rate for a multidimensional system
492
14.3.4
Some observations
496
14.3.5
TST for nonadiabatic transitions
497
14.3.6
TST with tunneling 4
14.4
Dynamical effects in barrier crossing The Kramers model
499
14.4.1
Escape from a one-dimensional well
500
14.4.2
The overdamped case DV/L
14.4.3
Moderate-to-large damping
505
14.4.4
The low damping limit
508
14.5
Observations and extensions Dlz
14.5.1
Implications and shortcomings of the Kramers theory
513
14.5.2
Non-
Markov
і
an effects
516
14.5.3
The normal mode representation
51ο
14.6
Some experimental observations -^
14.7
Numerical simulation of barrier crossing
523
14.8
Diffusion-controlled reactions DZ/
14A Solution of Eqs
(14.62)
and
(14.63)
531
14B Derivation of the energy Smoluchowski equation
533
15
Solvation dynamics
536
15.1
Dielectric solvation
537
15.2
Solvation in a continuum dielectric environment
5-3
15.2.1
General observations
-*
15.2.2
Dielectric relaxation and the Debye model 54U
15.3
Linear response theory of solvation
543
15.4
More aspects of solvation dynamics 546
15.5
Quantum solvation
549
16
Electron transfer processes
552
16.1
Introduction
552
16.2
A primitive model
555
16.3
Continuum dielectric theory of electron transfer processes
559
16.3.1
The problem 559
16.3.2
Equilibrium electrostatics 5
CONTHNTS
ХХІ
16.3.3
Transition assisted by dielectric fluctuations
561
16.3.4
Thermodynamics with restrictions
561
16.3.5
Dielectric fluctuations
562
16.3.6
Energetics of electron transfer between two
ionic centers
567
16.3.7
The electron transfer rate
570
16.4
A molecular theory of the nonadiabatic electron transfer rate
570
16.5
Comparison with experimental results
574
16.6
Solvent-controlled electron transfer dynamics
577
16.7
A general expression for the dielectric reorganization energy
579
16.8
The Marcus parabolas
581
16.9
Harmonic field representation of dielectric response
582
16.10
The nonadiabatic coupling
588
16.11
The distance dependence of electron transfer rates
589
16.12
Bridge-mediated long-range electron transfer
591
16.13
Electron tranport by hopping
596
16.14
Proton transfer
600
16A Derivation of the Mulliken-Hush formula
602
17
Electron transfer and transmission at molecule-metal and
molecule-semiconductor interfaces
607
17.1
Electrochemical electron transfer
607
17.1.1
Introduction
607
17.1.2
The electrochemical measurement
609
17.1.3
The electron transfer process
611
17.1.4
The nuclear reorganization
614
17.1.5
Dependence on the electrode potential:
Tafel
plots
614
17.1.6
Electron transfer at the semiconductor-electrolyte
interface
616
17.2
Molecular conduction
618
17.2.1
Electronic structure models of molecular conduction
619
17.2.2
Conduction of a molecular junction
621
17.2.3
The bias potential
625
17.2.4
The one-level bridge model
626
17.2.5
A bridge with several independent levels
629
17.2.6
Experimental statistics
632
17.2.7
The tight-binding bridge model
633
18
Spectroscopy
640
18.1
Introduction
641
18.2
Molecular spectroscopy in the dressed-state picture
643
Xxii
CoNIIMS
18.3
Resonance Raman scattering
651
18.4
Resonance energy transfer
656
18.5
Thermal relaxation and dephasing
664
18.5.1
The Bloch equations
665
18.5.2
Relaxation of a prepared state
665
18.5.3
Dephasing (decoherence)
666
18.5.4
The absorption lineshape
667
18.5.5
Homogeneous and inhomogeneous broadening
668
18.5.6
Motional narrowing
670
18.5.7
Thermal effects in resonanee Raman scattering
674
18.5.8
A case study: Resonance Raman scattering and
fluorescence from
Л
/ulene
in a Naphtalcne matrix
679
18.6
Probing inhomogeneous bands
682
18.6.1
Hole burning spectroscopy
683
18.6.2
Photon echoes
685
18.6.3
Single molecule spectroscopy
689
18.7
Optical response functions
691
18.7.1
The Hamiltonian
692
18.7.2
Response functions at the single molecule level
693
18.7.3
Many body response theory
696
18.7.4
Independent particles
698
18.7.5
Linear response
699
18.7.6
Linear response theory of propagation and
absorption
701
18A Steady-state solution of Eqs
(18.58):
the Raman scattering flux
703
Index
709
|
| any_adam_object | 1 |
| author | Nitzan, Abraham 1944- |
| author_GND | (DE-588)131744593 |
| author_facet | Nitzan, Abraham 1944- |
| author_role | aut |
| author_sort | Nitzan, Abraham 1944- |
| author_variant | a n an |
| building | Verbundindex |
| bvnumber | BV041772310 |
| classification_rvk | VE 5800 VE 9400 |
| ctrlnum | (OCoLC)885229357 (DE-599)BSZ395150051 |
| dewey-full | 541.394 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 541 - Physical chemistry |
| dewey-raw | 541.394 |
| dewey-search | 541.394 |
| dewey-sort | 3541.394 |
| dewey-tens | 540 - Chemistry and allied sciences |
| discipline | Chemie / Pharmazie |
| edition | 1. publ. in paperback |
| format | Book |
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| id | DE-604.BV041772310 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T01:05:02Z |
| institution | BVB |
| isbn | 9780199686681 9780198529798 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027218276 |
| oclc_num | 885229357 |
| open_access_boolean | |
| owner | DE-703 DE-355 DE-BY-UBR DE-19 DE-BY-UBM |
| owner_facet | DE-703 DE-355 DE-BY-UBR DE-19 DE-BY-UBM |
| physical | XXII, 719 S. graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| series2 | Oxford graduate texts |
| spelling | Nitzan, Abraham 1944- Verfasser (DE-588)131744593 aut Chemical dynamics in condensed phases relaxation, transfer and reactions in condensed molecular systems Abraham Nitzan 1. publ. in paperback Oxford [u.a.] Oxford Univ. Press 2013 XXII, 719 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford graduate texts Molecular dynamics Chemical reaction, Conditions and laws of Chemische Reaktion (DE-588)4009853-9 gnd rswk-swf Molekulardynamik (DE-588)4170370-4 gnd rswk-swf Kondensierte Materie (DE-588)4132810-3 gnd rswk-swf Molekulardynamik (DE-588)4170370-4 s Chemische Reaktion (DE-588)4009853-9 s Kondensierte Materie (DE-588)4132810-3 s 1\p DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027218276&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Nitzan, Abraham 1944- Chemical dynamics in condensed phases relaxation, transfer and reactions in condensed molecular systems Molecular dynamics Chemical reaction, Conditions and laws of Chemische Reaktion (DE-588)4009853-9 gnd Molekulardynamik (DE-588)4170370-4 gnd Kondensierte Materie (DE-588)4132810-3 gnd |
| subject_GND | (DE-588)4009853-9 (DE-588)4170370-4 (DE-588)4132810-3 |
| title | Chemical dynamics in condensed phases relaxation, transfer and reactions in condensed molecular systems |
| title_auth | Chemical dynamics in condensed phases relaxation, transfer and reactions in condensed molecular systems |
| title_exact_search | Chemical dynamics in condensed phases relaxation, transfer and reactions in condensed molecular systems |
| title_full | Chemical dynamics in condensed phases relaxation, transfer and reactions in condensed molecular systems Abraham Nitzan |
| title_fullStr | Chemical dynamics in condensed phases relaxation, transfer and reactions in condensed molecular systems Abraham Nitzan |
| title_full_unstemmed | Chemical dynamics in condensed phases relaxation, transfer and reactions in condensed molecular systems Abraham Nitzan |
| title_short | Chemical dynamics in condensed phases |
| title_sort | chemical dynamics in condensed phases relaxation transfer and reactions in condensed molecular systems |
| title_sub | relaxation, transfer and reactions in condensed molecular systems |
| topic | Molecular dynamics Chemical reaction, Conditions and laws of Chemische Reaktion (DE-588)4009853-9 gnd Molekulardynamik (DE-588)4170370-4 gnd Kondensierte Materie (DE-588)4132810-3 gnd |
| topic_facet | Molecular dynamics Chemical reaction, Conditions and laws of Chemische Reaktion Molekulardynamik Kondensierte Materie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027218276&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT nitzanabraham chemicaldynamicsincondensedphasesrelaxationtransferandreactionsincondensedmolecularsystems |